Question

A quadratic polynomial is such that the sum and product of its zeroes are $\frac{21}{8},\frac{5}{16}$ respectively. Find its zeroes.

• A.
  $\frac{7}{2},\frac{-1}{6}$
• B.
  $\frac{5}{2},\frac{1}{8}$
• C.
  $\frac{3}{2},\frac{3}{7}$
• D.
  $\frac{3}{4},\frac{2}{9}$

Answer 1

The correct option is B

$\frac{5}{2},\frac{1}{8}$

Given,
Sum of the zeros (S) $=\frac{21}{8}$
Product of the zeros (P) $=\frac{5}{16}$
The, the required polynomial is given,
$p\left(x\right)=k(x^2-Sx+P)$
$=>p\left(x\right)=k(x^2-\frac{21}{8}x+\frac{5}{16})$
$=>p\left(x\right)=\frac{k}{16}(16x^2-42x+5)$
where $k$ is a non zero real number
Zeros of the polynomial are
$p\left(x\right)=0$
$=>\frac{k}{16}(16x^2-42x+5)=0$
$=>16x^2-42x+5=0$
$=>16x^2-40x-2x+5=0$
$=>8x(2x-5)-(2x-5)=0$
$=>(8x-1)(2x-5)=0$
$=>x=\frac{1}{8}$ or $x=\frac{5}{2}$
Thus, the zeros are $\frac{1}{8}$ and $\frac{5}{2}$